copyright © 2008 pearson addison-wesley. all rights reserved. chapter 5 modern portfolio concepts

Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Chapter 5

Modern Portfolio Concepts

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-2


• Learning Goals

1. Understand portfolio objectives and the procedures used to calculate portfolio return and standard deviation.

2. Discuss the concepts of correlation and diversification, and the key aspects of international diversification.

3. Describe the components of risk and the use of beta to measure risk.



• Learning Goals (cont’d)

4. Explain the capital asset pricing model (CAPM) – conceptually, mathematically, and graphically.

5. Review the traditional and modern approaches to portfolio management.

6. Describe portfolio betas, the risk-return tradeoff, and reconciliation of the two approaches to portfolio management.


What is a Portfolio?

• Portfolio is a collection of investment vehicles assembled to meet one or more investment goals.

• Growth-Oriented Portfolio: primary objective is long-term price appreciation

• Income-Oriented Portfolio: primary objective is current dividend and interest income


The Ultimate Goal: An Efficient Portfolio

• Efficient portfolio

– A portfolio that provides the highest return for a given level of risk, or

– Has the lowest risk for a given level of return


Portfolio Return and Risk Measures

• Return on a Portfolio is the weighted average of returns on the individual assets in the portfolio

• Standard Deviation of a portfolio’s returns is calculated using all of the individual assets in the portfolio


Return on Portfolio

Returnon

portfolio=

Proportion ofportfolio's total

dollar valuerepresented by

asset 1

⎛

⎝

⎜⎜⎜⎜

×Returnon asset

1

⎞

⎠

⎟⎟⎟⎟⎟

+



asset 2

×Returnon asset

2

⎞

⎠

⎟⎟⎟⎟

⎛

⎝

⎜⎜⎜⎜⎜

+ L +



asset n

×Return on asset

n

⎞

⎠

⎟⎟⎟⎟

⎛

⎝

⎜⎜⎜⎜⎜

=j =1

n∑



asset j

⎛

⎝

⎜⎜⎜⎜

×Returnon asset

j

⎞

⎠

⎟⎟⎟⎟⎟

rp = w1 × r1( ) + w2 × r2( ) + L + wn × rn( ) = wj × rj( )

j=1

n

∑


Correlation: Why Diversification Works!

• Correlation is a statistical measure of the relationship between two series of numbers representing data

• Positively Correlated items move in the same direction

• Negatively Correlated items move in opposite directions

• Correlation Coefficient is a measure of the degree of correlation between two series of numbers representing data


Correlation Coefficients

• Perfectly Positively Correlated describes two positively correlated series having a correlation coefficient of +1

• Perfectly Negatively Correlated describes two negatively correlated series having a correlation coefficient of -1

• Uncorrelated describes two series that lack any relationship and have a correlation coefficient of nearly zero


Figure 5.1 The Correlation Between Series M, N, and P


Correlation: Why Diversification Works!

• To reduce overall risk in a portfolio, it is best to combine assets that have a negative (or low-positive) correlation

• Uncorrelated assets reduce risk somewhat, but not as effectively as combining negatively correlated assets

• Investing in different investments with high positive correlation will not provide sufficient diversification


Figure 5.2 Combining Negatively Correlated Assets to Diversify Risk


Table 5.3 Correlation, Return, and Risk for Various Two-Asset Portfolio Combinations


Why Use International Diversification?

• Offers more diverse investment alternatives than U.S.-only based investing

• Foreign economic cycles may move independently from U.S. economic cycle

• Foreign markets may not be as “efficient” as U.S. markets, allowing true gains from superior research

• Study done between 1984 and 1994 suggests that portfolio 70% S&P 500 and 30% EAFE would reduce risk 5% and increase return 7% over a 100% S&P 500 portfolio


International Diversification

• Advantages of International Diversification– Broader investment choices– Potentially greater returns than in U.S.– Reduction of overall portfolio risk

• Disadvantages of International Diversification– Currency exchange risk– Less convenient to invest than U.S. stocks– More expensive to invest– Riskier than investing in U.S.


Methods of International Diversification

• Foreign company stocks listed on U.S. stock exchanges– Yankee Bonds– American Depository Shares (ADS’s)– Mutual funds investing in foreign stocks– U.S. multinational companies (typically not

considered a true international investment for diversification purposes)


Components of Risk

• Diversifiable (Unsystematic) Risk– Results from uncontrollable or random events that are

firm-specific– Can be eliminated through diversification– Examples: labor strikes, lawsuits

• Nondiversifiable (Systematic) Risk– Attributable to forces that affect all similar investments– Cannot be eliminated through diversification – Examples: war, inflation, political events


Components of Risk

Total risk = Nondiversifiable risk + Diversifiable risk


Beta: A Popular Measure of Risk

• A measure of nondiversifiable risk• Indicates how the price of a security responds to market forces• Compares historical return of an investment to the market return (the

S&P 500 Index)• The beta for the market is 1.00• Stocks may have positive or negative betas. Nearly all are positive.• Stocks with betas greater than 1.00 are more risky than the overall

market.• Stocks with betas less than 1.00 are less risky than the overall market.


Beta: A Popular Measure of Risk

Table 5.4 Selected Betas and Associated Interpretations


Interpreting Beta

• Higher stock betas should result in higher expected returns due to greater risk

• If the market is expected to increase 10%, a stock with a beta of 1.50 is expected to increase 15%

• If the market went down 8%, then a stock with a beta of 0.50 should only decrease by about 4%

• Beta values for specific stocks can be obtained from Value Line reports or online websites such as yahoo.com


Interpreting Beta


Capital Asset Pricing Model (CAPM)

• Model that links the notions of risk and return

• Helps investors define the required return on an investment

• As beta increases, the required return for a given investment increases


Capital Asset Pricing Model (CAPM) (cont’d)

• Uses beta, the risk-free rate and the market return to define the required return onan investment

Required returnon investment j

= Risk-free rate +Beta for

investment j⎡⎣⎢

×Marketreturn

−Risk-free

rate⎛⎝⎜

⎞⎠⎟⎤⎦⎥


Capital Asset Pricing Model (CAPM) (cont’d)

• CAPM can also be shown as a graph

• Security Market Line (SML) is the “picture” of the CAPM

• Find the SML by calculating the required return for a number of betas, then plotting them on a graph


Figure 5.6 The Security Market Line (SML)


Two Approaches to Constructing Portfolios

Traditional Approachversus

Modern Portfolio Theory


Traditional Approach

• Emphasizes “balancing” the portfolio using a wide variety of stocks and/or bonds

• Uses a broad range of industries to diversify the portfolio

• Tends to focus on well-known companies– Perceived as less risky– Stocks are more liquid and available– Familiarity provides higher “comfort” levels

for investors


Modern Portfolio Theory (MPT)

• Emphasizes statistical measures to develop a portfolio plan

• Focus is on:– Expected returns– Standard deviation of returns– Correlation between returns

• Combines securities that have negative (or low-positive) correlations between each other’s rates of return


Key Aspects of MPT: Efficient Frontier

• Efficient Frontier

– The leftmost boundary of the feasible set of portfolios that include all efficient portfolios: those providing the best attainable tradeoff between risk and return

– Portfolios that fall to the right of the efficient frontier are not desirable because their risk return tradeoffs are inferior

– Portfolios that fall to the left of the efficient frontier are not available for investments


Figure 5.7 The Feasible or Attainable Set and the Efficient Frontier


Key Aspects of MPT: Portfolio Betas

• Portfolio Beta

– The beta of a portfolio; calculated as the weighted average of the betas of the individual assets the portfolio includes

– To earn more return, one must bear more risk

– Only nondiversifiable risk (relevant risk) provides a positive risk-return relationship


Key Aspects of MPT: Portfolio Betas

Table 5.6 Austin Fund’s Portfolios V and W


Figure 5.8 Portfolio Risk and Diversification


Interpreting Portfolio Betas

• Portfolio betas are interpreted exactly the same way as individual stock betas.– Portfolio beta of 1.00 will experience a 10% increase when the

market increase is 10%– Portfolio beta of 0.75 will experience a 7.5% increase when the

market increase is 10%– Portfolio beta of 1.25 will experience a 12.5% increase when the

market increase is 10%

• Low-beta portfolios are less responsive and less risky than high-beta portfolios.

• A portfolio containing low-beta assets will have a low beta, and vice versa.


Interpreting Portfolio Betas

Table 5.7 Portfolio Betas and Associated Changes in Returns


Reconciling the Traditional Approach and MPT

• Recommended portfolio management policy uses aspects of both approaches:

– Determine how much risk you are willing to bear

– Seek diversification between different types of securities and industry lines

– Pay attention to correlation of return between securities

– Use beta to keep portfolio at acceptable level of risk

– Evaluate alternative portfolios to select highest return for the given level of acceptable risk


Figure 5.9 The Portfolio Risk-Return Tradeoff


Chapter 5 Review

• Learning Goals

1. Understand portfolio objectives and the procedures used to calculate portfolio return and standard deviation.

2. Discuss the concepts of correlation and diversification, and the key aspects of international diversification.

3. Describe the components of risk and the use of beta to measure risk.


Chapter 5 Review (cont’d)

• Learning Goals (cont’d)

4. Explain the capital asset pricing model (CAPM) – conceptually, mathematically, and graphically.

5. Review the traditional and modern approaches to portfolio management.

6. Describe portfolio betas, the risk-return tradeoff, and reconciliation of the two approaches to portfolio management.


Table 5.1 Expected Return, Average Return, and Standard Deviation of Returns for Portfolio XY


Table 5.2 Expected Returns, Average Returns, and Standard Deviations for Assets X, Y, and Z and Portfolios XY and XZ


Figure 5.4 Risk and Return for AllCombinations of Assets A and B for Various Correlation Coefficients


Table 5.5 The Growth Fund of America, August 31, 2005

copyright © 2008 pearson addison-wesley. all rights reserved. chapter 5 modern portfolio concepts

Documents

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